1) Gathering the data
221 people = 65%
2) To find the 100% people surveyed let's set a direct proportion. And then cross multiply to have an equation:
% people
65-----------221
100-------- y
65y = 22100 Dividing both sides by 65
y =340
So, 340 people were surveyed.
There are 7 balls numbered I through 7 placed in a bucket What is the probability of reaching into the bucket and randomly drawing two balls numbered 6 and 3 without replacement, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
We have:
- Numbers of balls from 1 to 7 = 7
- Number of balls with number 6 = 1
- Number of ball with number 3 = 1
Then, the probability of ramdomly choosing a 6 is
[tex]p(6)=\frac{1}{7}[/tex]Once we chose a ball, there are 6 balls into the bucket. Then the probability of ramdomly choosing a 3 is
[tex]P(3)=\frac{1}{6}[/tex]Then, the probability of randomly choosing a 6 and 3 in that order, is
[tex]\begin{gathered} P(6\text{and}3)=P(6)\cdot P(3)=\frac{1}{7}\cdot\frac{1}{6} \\ P(6\text{ and 3)=}\frac{1}{7\cdot6} \\ P(6\text{ and 3)=}\frac{1}{42} \end{gathered}[/tex]that is, the probability is 1/42 = 0.023809
f(x) = 3x2 + 4x – 6g(x) = 6x3 – 522 – 2Find (f - g)(x).O A. (f - g)(x) = -6x3 + 8x2 + 4x – 4O B. (f - g)(x) = 623 – 2x² + 4x - 8O C. (f - g)(x) = 6x3 – 8x2 - 4x + 4O D. (f - g)(x) = -6x3 – 2x2 + 4x – 8SUBMIT
We are being asked to subtract one function from another function.
[tex](f-g)(x)=f(x)-g(x)[/tex][tex]\begin{gathered} (f-g)(x)=(3x^2+4x-6)-(6x^3-5x^2-2)=3x^2+4x-6-6x^3+5x^2+2 \\ (f-g)(x)=-6x^3+8x^2+4x-4 \end{gathered}[/tex]Answer: .
Giving a test to a group of students, the grades and gender are summarized belowIf one student is chosen at random,Find the probability that the student was male OR got a(n) "A". (Please enter a reduced fraction.)
To find the probability that the student was male or got an A, we have to find the probabilities that the student was male (event A), got an A (event B) and the intersection between these events (A∩B).
[tex]P(A)=\frac{48}{75}=\frac{16}{25}[/tex][tex]P(B)=\frac{26}{75}[/tex][tex]P(A\cap B)=\frac{12}{75}=\frac{4}{25}[/tex]Now, to find the asked probability, use the following formula:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=\frac{48}{75}+\frac{26}{75}-\frac{12}{75} \\ P(A\cup B)=\frac{62}{75} \end{gathered}[/tex]The answer is 62/75.
Slove for x Cosec(x-20°)=2/√3
The trignometric ratio is x Cosec(x-20°)=2/√3 is x = 80°.
What is trigonometry as it is a ratio?Trigonometric: A ratio is the sum of the values of all trigonometric functions whose values depend on the ratio of the sides of a right-angled triangle.The trigonometric ratio of a right-angled triangle is determined by the ratio of the triangle's sides to any acute angle.Metric and trigon are the respective Greek words for measurement and triangle.Right triangles have a 90° angle, and trigonometric ratios are specific measurements of these triangles.Now, calculate the trigonometric ratio as follows:
cosec(x-20) = 2/√3cosec ( x-20) = cosec ( 60 )x - 20 = 60x = 80°Therefore, the trignometric ratio is x Cosec(x-20°)=2/√3 is x = 80°.
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Four times a number b is six times the sum of b and five
The number b is -15
Here, we want to write an equation and solve it
We go step by step
Four times a number b
= 4 * b = 4b
is six times the sum of b and 5
The sum of b and 5 is b+ 5
six times this is = 6(b + 5)
Now euating the two, we have;
4b = 6(b + 5)
4b = 6b + 30
collect like terms
6b - 4b = -30
2b = -30
b = -30/2
b = -15
What is the image of (-6, -2) after a dilation by a scale factor of 4 centered at theorigin?
The image of (-6, -2) after dilation by a scale of 4 is (-24, -8)
Explanation:The image of (-6, -2) after dilation by a scale of 4 is
(-6*4, -2*4)
= (-24, -8)
It walks for 37.5 meters at a speed of 3 meters per minute. For how many minutes does it walk?
Data
• distance: 37.5 meters
,• speed: 3 meters/minute
,• time: ? minutes
,•
From definition:
speed = distance/time
Replacing with data, and solving for time:
3 = 37.5/time
time = 37.5/3
time = 12.5 minutes
sketch the angle then find its reference angle [tex] \frac{13\pi}{4} [/tex]
We need to find the reference angle by sketching the angle:
First, we need to subtract it by 2π, then:
[tex]θ=\frac{13\pi}{4}-2\pi=\frac{5}{4}\pi[/tex]Hence, the reference angle is 5π / 4.
Write the equation of a function that has the given characteristics.The graph of y = |x|, shifted 8 units upwardоа y = |x-81y = |x+81y = x| + 8y = |x| - 8
The given function is
[tex]y=|x|[/tex]The transformation is shifted 8 units upwards.
Remember, to move the function upwards we have to sum outside the absolute value bars.
Therefore, the transformed function would be
[tex]y=|x|+8[/tex]Michael monthly salary after tax is 2,675 if Michele pays for rent,food,and other Bill's totaling 2,140 then how much money is left
We are told that Michael has a total of $2675. If he spends $2140, then the total amount left is the difference between the total and the spent amount, that is:
[tex]2645-2140=505[/tex]Therefore, he has $505 left.
How would you change 65% to a decimal?
In converting percentage to decimals, you need to divide it by 100.
[tex]\frac{65}{100}=0.65[/tex]The answer is 0.65
Write an equation and graph the cosine function with amplitude 3 and period 4 pi.
An equation and graph the cosine function with amplitude 3 and period 4 pi is y is 3cos([tex]\frac{1}{2} x[/tex])
How to write an equation ?
The general form for the cosine function is:
y = A cos(Bx+C)+D
The amplitude is:
|A|
The period is:
P = 2π/B
The phase shift is
ϕ = −C/B
The vertical shift is D
Explanation:
Given:
The amplitude is 3:
|A|=3
The above implies that A could be either positive or negative but we always choose the positive value because the negative value introduces a phase shift:
A=3
Given:
The period is
P = 4π
4π =2π/B
B = 1/2
Nothing is said about the phase shift and the vertical shift, therefore, we shall assume that
C and D are 0.
Substitute these values into the general form:
y = 3cos([tex]\frac{1}{2} x[/tex])
An equation and graph the cosine function with amplitude 3 and period 4 pi is y is 3cos([tex]\frac{1}{2} x[/tex])
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I will show you the pic
Part b
we have
2y=-x-8
Remember that
the equation in slope intercept form is
y=mx+b
so
Isolate the variable y
divide by 2 both sides
2y/2=-(x/2)-8/2
y=-(1/2)x-4Part c
we have
y-4=-3(x-3)
apply distributive property right side
y-4=-3x+9
Adds 4 both sides
y=-3x+9+4
y=-3x+13And the surface area of each hemisphere below.7.8C
The surface area of the hemisphere is computed using the equation
[tex]SA=3\pi r^2[/tex]For the hemisphere with a radius of 14 yds, the surface area of the hemisphere is
[tex]SA=3\pi(14)^2=588\pi[/tex]For the hemisphere with a diameter of 12.2 yds, we need to find its radius first. The radius is just half of the diameter, hence, the radius of this hemisphere is 6.1 yds. Computing for its surface area, we have
[tex]SA=3\pi(6.1)^2=111.63\pi[/tex]You have one type of chocolate that sells for $5.00/lb and another type of chocolate that sells for $7.60/lb. You would like to have 10.4 lbs of a chocolate mixture that sells for $6.50/lb. How much of each chocolate will you need to obtain the desired mixture? You will need BLANK lbs of the cheaper chocolate and BLANK lbs of the expensive chocolate.Please help!! It is urgent.
Answer
You will need 4.4 lbs of the cheaper chocolate and 6 lbs of the expensive chocolate.
Explanation
Let the amount to be made of the type of chocolate (cheaper chocolate) that sells for $5.00/lb be x pounds.
Let the amount to be made of the type of chocolate (expensive chocolate) that sells for $7.60/lb be y pounds.
We would like to make a chocolate mixture that weighs 10.4 lbs. That is,
x + y = 10.4 .......... equation 1
This chocolate mixture is supposed to cost $6.50/lb and weigh 10.4 lbs. Hence, the cost of 10.4 lbs of this chocolate mixture will be
= 6.50 × 10.4 = $67.6
The cost of x pounds of the $5.00/lb = x × 5 = 5x dollars
The cost of y pounds of the $7.60/lb = y × 7.60 = 7.6y dollars
The cost of the two types of chocolate have to amount to $67.6
5x + 7.6y = 67.6 .......... equation 2
Writing the two equations together
x + y = 10.4
5x + 7.6y = 67.6
This simultaneous equation is then solved and the solution obtained is
x = 4.4 pounds and y = 6 pounds.
Hope this Helps!!!
A) Graph the ellipse. Use graph paper or sketch neatly on regular paper. The ellipse must be hand drawn - no computer tools or graphing calculator. Give the center of the ellipse. Give the vertices of the ellipse. Give the endpoints of the minor axis. Give the foci.
The general equation of an ellipse is:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1.[/tex]Where:
• (h, k) are the coordinates of the centre,
,• a and b are the lengths of the legs.
The parts of the ellipse are:
In this case, we have the equation:
[tex]\frac{(x+1)^2}{5^2}+\frac{(y-4)^2}{4^2}=1.[/tex]So we have:
• (h, k) = (-1, 4),
,• a = 5,
,• b = 4.
A) The graph of the ellipse is:
B) The center of the ellipse is (h, k) = (-1, 4).
C) The vertices of the ellipse are:
• (h + a, k) = (-1 + 5, 4) = ,(4, 4),,
,• (h - a, k) = (-1 - 5, 4) =, (-6, 4),,
D) The endpoints of the minor axis are:
• (h, k + b) = (-1, 4 + 4 ) = ,(-1, 8),,
,• (h, k - b) = (-1, 4 - 4) = ,(-1, 0),.
E) To find the focuses, we compute c:
[tex]c=\sqrt[]{a^2-b^2}=\sqrt[]{5^2-4^2}=\sqrt[]{25-16}=\sqrt[]{9}=3.[/tex]The focuses of the ellipse are:
• (h + c, k) = (-1 + 3, 4) = ,(2, 4),,
,• (h - c, k) = (-1 - 3, 4) = ,(-4, 4),.
Answer
A)
B) (-1, 4)
C) (4, 4), (-6, 4)
D) (-1, 8), (-1, 0)
E) (2, 4), (-4, 4)
Kim owes her friend $235 and plans to pay $5 per week. Select the equation of the function that shows
Answer:
The function is: y = 235 - 5x
x-intercept: 47
y-intercept: 235
The x-intercept means that it takes Kim 47 weeks to pay all of her debt.
The y-intercept means that Kim owes her friend $235.
Step-by-step explanation:
The amount that Kim owes her friend after x weeks is given by the following function:
y = b - ax
In which b is the initial amount she owes and a is how much she pays per week.
Kim owes her friend $235 and plans to pay $5 per week.
So b = 235, a = 5.
The function is: y = 235 - 5x
x-intercept:
Value of x when y = 0, that is, the amount of weeks it takes for her to pay all her debt.
So
235 - 5x = 0
5x = 235
x = 235/5
x = 47
x-intercept: 47
The x-intercept means that it takes Kim 47 weeks to pay all of her debt.
y-intercept:
Value of y when x = 0, that is, the total amount that Kim owes.
235 - 5*0 = 235
y-intercept: 235
The y-intercept means that Kim owes her friend $235.
Which two expressions are equivalent?A. A(0.52)-21B. A(1.04)-C. A(0.96)D. A(0.96 0.08
Equivalent expressions are expressions that have the values when we put the same values for the variables.
From the given expressions, let's find the equivalent expressions.
From the given expressions, let's substitute 1 for t and evaluate.
The expressions with the same result will be equivalent expressions.
[tex]\begin{gathered} A(0.52)^{-2t} \\ \\ A(0.52)^{-2(1)} \\ \\ A(0.52)^{-2} \\ \\ A(\frac{1}{0.52^2}) \\ \\ A(\frac{1}{0.274}) \\ \\ =3.698A \end{gathered}[/tex][tex]\begin{gathered} A(1.04)^{-t}_{} \\ \\ A(1.04)^{-1} \\ \\ A(\frac{1}{1.04}) \\ \\ A(0.96) \\ \\ =0.96A \end{gathered}[/tex][tex]\begin{gathered} A(0.96)^t \\ \\ A(0.96)^1 \\ \\ A(0.96) \\ \\ =0.96A \end{gathered}[/tex][tex]\begin{gathered} A(0.96)^{0.08t}^{} \\ \\ A(0.96)^{0.08(1)} \\ \\ A(0.96)^{0.08} \\ \\ A(0.998) \\ \\ =0.998A \end{gathered}[/tex]The expressions with the same result are the expressions in options B and C:
[tex]\begin{gathered} B.A(1.04)^{-t} \\ \\ C.A(1.96)^t \end{gathered}[/tex]Therefore, the two expressions that are equivalent are:
[tex]\begin{gathered} B.A(1.04)^{-t} \\ \\ C.A(1.96)^t \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} \text{ B. A(1.04})^{-t} \\ \\ \text{ C. A(1.96)}^t \end{gathered}[/tex]Roxanne likes to fish. She estimates that 30% of the fish she catches are trout, 20% are bass, and 10% are perch. She designs a simulation.Let 0, 1, and 2 represent trout.Let 3 and 4 represent bass,Let 5 represent perch.Let 6, 7, 8, and 9 represent other fish.The table shows the simulation results. what is the estimated probability that at least one of the next four roxanne catches will be bass?
We have 20 equally probable events in the table. So, each box has probability equal to 1/20.
With this in mind, we must find the numbers 3 and 4 in each box. Then, we can see that there are 12 boxes containing these numbers. Therefore, the probability to catch a bass is
[tex]\begin{gathered} P(\text{bass)}=12\cdot(\frac{1}{20}) \\ P(\text{bass)}=\frac{12}{20} \\ P(\text{bass)}=\frac{3}{5} \end{gathered}[/tex]By converting these result in percentage, we have
[tex]\frac{3}{5}\cdot100=60[/tex]that is, 60% could be bass fish.
What is the volume of the cone? 1 Use the formula 1 = 6 cm 1 1 18 cm 1 1 1 1 A 16-em> or < 50.3 cm B) 32cm or 100.5 CMS 8 cm or
can someone help me with this math problem a write a number line to it
POSSIBLE Match the function rule to the table of values. f(x)=2 х f (x) = (3) f(x) = 32 2 f () = ( 1 ) 28
First, we must evaluate each function at the given values of x.
When x=-2, we have
[tex]\begin{gathered} f(x)=2^x\Rightarrow f(-2)=2^{-2}=\frac{1}{2^2}=\frac{1}{4}=0.25 \\ \end{gathered}[/tex][tex]f(x)=(\frac{1}{3})^x\Rightarrow f(-2)=(\frac{1}{3})^{-2}=\frac{1}{3^{-2}}=3^2=9[/tex][tex]f(x)=3^x\Rightarrow f(-2)=3^{-2}=\frac{1}{3^2}=\frac{1}{9}=0.11[/tex][tex]f(x)=(\frac{1}{2})^x\Rightarrow f(-2)=(\frac{1}{2})^{-2}=\frac{1}{2^{-2}}=2^2=4[/tex]Now, we must compare these result with the tables. Then the solutions are:
-2x^3 - 10y-7 evaluate if x = 4 and y = -9
We are given the following expression:
[tex]-2x^3-10y-7[/tex]We are asked to evaluate the expression in the following points:
[tex]\begin{gathered} x=4 \\ y=-9 \end{gathered}[/tex]To determine the value of the expression we will substitute the value in the expression like this;
[tex]-2(4)^3-10(-9)-7[/tex]Now, we solve the exponents:
[tex]-2(4)^3-10(-9)-7=-2(64)-10(-9)-7[/tex]Now, we solve the products:
[tex]-2(64)-10(-9)-7=-128+90-7[/tex]Solving the operations:
[tex]-128+90-7=-45[/tex]Therefore, the numerical value is -45
Can you please help me
The formula to calculate the volume of a prism is given as
[tex]V=\text{Base Area }\times Height[/tex]The volume is given as 45 and the height is 9.
Hence, we can get the base area as
[tex]\begin{gathered} A=\frac{V}{h} \\ A=\frac{45}{9} \\ A=5 \end{gathered}[/tex]Therefore, the area of the base is 5 ft².
The correct option is OPTION B.
instructions for building a polynomial roller coaster in factored form
The polynomial that is used to represent the roller coaster in factored form is y = +a x (x- 500) (x- 1000)
The given conditions are.
The negative intercept at x = 500
the roller coaster passes through the x-axis at x=0 and at x=1000
The polynomial equation is of the form will be
y = a x (x- 500) (x- 1000)
The polynomial will have a root at x=0 , at x=500 and at x = 1000
Polynomials are used in many areas of mathematics and science. For instance, they are employed in calculus, but numerical analysis is used to approximate other functions instead.
Polynomial functions are used in a variety of situations, from basic physics and biology to economics and social science. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a wide range of topics.
Polynomials are used in higher mathematics to construct algebraic varieties and polynomial rings, two key concepts in algebra and algebraic geometry with the use of variables.
Therefore the polynomial that is used to represent the roller coaster in factored form is y = a x (x- 500) (x- 1000)
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Solve this system of equations byusing the elimination method.3x + 3y = 182x + y = 4( [?]. []).
Given the system of equations:
3x + 3y = 18
2x + y = 4
Let's solve the system of equations using the elimination method.
Multiply one equation by a number which makes one variable of each equation opposite.
Multiply equation 2 by -3:
3x + 3y = 18
-3(2x + y) = -3(4)
3x + 3y = 18
-6x - 3y = -12
Add both equations:
3x + 3y = 18
+ -6x - 3y = -12
_________________
-3x = 6
Divide both sides by -3:
[tex]\begin{gathered} \frac{-3x}{-3}=\frac{6}{-3} \\ \\ x=-2 \end{gathered}[/tex]Substitute -2 for x in either of the equations.
Take the second equation:
2x + y = 4
2(-2) + y = 4
-4 + y = 4
Add 4 to both sides:
-4 + 4 + y = 4 + 4
y = 8
Therefore, we have the solutions:
x = -2, y = 8
In point form, we have the solution:
(x, y) ==> (-2, 8)
ANSWER:
(-2, 8)
Let f(x)=V3x and g(x)=×6. What'sthe smallest number that is in the domain off° g?
Answer:
Explanation:
Given:
[tex]\begin{gathered} f(x)\text{ = }\sqrt{3x} \\ g(x)\text{ = x - 6} \end{gathered}[/tex]To find:
the domain of f o g
fog = (f o g)(x) = f(g(x))
First, we will substitute the expression in g(x) with x in f(x)
[tex][/tex]The measure of angle 1 is greater than 97 degrees and at most 115. Graph the possible values of x.
We are given the following:
Angle 1 is greater than 97 degrees and at most 115 degrees
The angle alternate to angle 1 is "(9x +7)"; alternate angles are congruent
Using the information above, we will develop the inequality shown below:
[tex]\begin{gathered} 97^{\circ}10 \\ x>10 \\ \\ \therefore x>10 \end{gathered}[/tex]We will proceed to the second portion of the inequality. We have:
[tex]\begin{gathered} (9x+7)\le115^{\circ} \\ 9x+7\le115 \\ \text{Subtract ''7'' from both sides, we have:} \\ 9x\le115-7 \\ 9x\le108 \\ \text{Divide both sides by ''9'', we have:} \\ \frac{9}{9}x\le\frac{108}{9} \\ x\le12 \\ \\ \therefore x\le12 \end{gathered}[/tex]We will combine both inequalities into one. We have it thus:
[tex]\begin{gathered} x>10 \\ x\le12 \\ \text{Combining the inequalities, we have:} \\ 10We will proceed to plot this inequality on the number line as shown below:Determine the amplitude, period, and phase shift for y=1/3tan (0 +30) and use them to plot the graph of the function.
Given: The function below
[tex]y=\frac{1}{3}tan(\theta+30^0)[/tex]To Determine: The amplitude, the period, and the phase shift
Solution
The graph of the function is as shown below
The general equation of a tangent function is
[tex]f(x)=Atan(Bx+C)+D[/tex]Where
[tex]\begin{gathered} A=Amplitude \\ Period=\frac{\pi}{B} \\ Phase-shift=-\frac{C}{B} \\ Vertical-shift=D \end{gathered}[/tex]Let us compare the general form to the given
[tex]\begin{gathered} y=\frac{1}{3}tan(\theta+30^0) \\ f(x)=Atan(B\theta+C)+D \\ A=\frac{1}{3} \\ B=1 \\ C=30^0 \\ D=0 \end{gathered}[/tex]Therefore
[tex]\begin{gathered} Amplitude=\frac{1}{3} \\ Period=\frac{\pi}{B}=\frac{180^0}{1}=180^0 \\ Phase-shift=-\frac{C}{B}=-\frac{30^0}{1}=-30^0 \end{gathered}[/tex]Hence, the correct option is as shown below
Question 18(1 point)Passes through the points, (0,6), (-8,6)What is the slope?
Given the coordinates of two points that passes through a line:
[tex]\text{ (0,6) and (-8,6)}[/tex]Let's name the points:
x1, y1 = -8,6
x2, y2 = 0,6
To be able to get the slope of the line (m), we will be using this formula:
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex]Let's plug in the coordinates to the formula to get the slope (m).
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]undefined[/tex]